O. Brivois, S. Bonelli, and R. Borghi, Soil erosion in the boundary layer flow along a slope: a theoretical study, European Journal of Mechanics - B/Fluids, vol.26, issue.6, pp.707-719, 2007.
DOI : 10.1016/j.euromechflu.2007.03.006

URL : https://hal.archives-ouvertes.fr/hal-00305325

S. Bonelli and O. Brivois, The scaling law in the hole erosion test with a constant pressure drop, International Journal for Numerical and Analytical Methods in Geomechanics, vol.80, issue.2, pp.1573-1595, 2008.
DOI : 10.1002/nag.683

URL : https://hal.archives-ouvertes.fr/hal-00305364

D. Lachouette, F. Golay, and S. Bonelli, One-dimensional modeling of piping flow erosion, Comptes Rendus M??canique, vol.336, issue.9, pp.731-736, 2008.
DOI : 10.1016/j.crme.2008.06.007

URL : https://hal.archives-ouvertes.fr/hal-00979078

P. Angot, C. Bruneau, and P. Fabrie, A penalization method to take into account obstacles in incompressible viscous flows, Numerische Mathematik, vol.81, issue.4, pp.497-520, 1999.
DOI : 10.1007/s002110050401

M. Foster and R. , Assessing Embankment Dam Filters That Do Not Satisfy Design Criteria, Journal of Geotechnical and Geoenvironmental Engineering, vol.127, issue.5, pp.398-407, 2001.
DOI : 10.1061/(ASCE)1090-0241(2001)127:5(398)

C. Wan and R. , Investigation of Rate of Erosion of Soils in Embankment Dams, Journal of Geotechnical and Geoenvironmental Engineering, vol.130, issue.4, pp.373-380, 2004.
DOI : 10.1061/(ASCE)1090-0241(2004)130:4(373)

P. Angot, Analysis of singular perturbations on the Brinkman problem for fictitious domain models of viscous flows, Mathematical Methods in the Applied Sciences, vol.1, issue.4, pp.1395-1412, 1999.
DOI : 10.1002/(SICI)1099-1476(19991110)22:16<1395::AID-MMA84>3.0.CO;2-3

C. Diaz-goano, P. D. Minev, and K. Nandakumar, A fictitious domain/finite element method for particulate flows, Journal of Computational Physics, vol.192, issue.1, pp.105-123, 2003.
DOI : 10.1016/S0021-9991(03)00349-8

K. Khadra, P. Angot, S. Parneix, and J. P. Caltagirone, Fictitious domain approach for numerical modelling of Navier-Stokes equations, International Journal for Numerical Methods in Fluids, vol.16, issue.8, pp.651-684, 2000.
DOI : 10.1002/1097-0363(20001230)34:8<651::AID-FLD61>3.0.CO;2-D

S. Osher and J. Sethian, Fronts propagating with curvature dependent speed: Algorithm for tracking material interface, J. Comput. Phys, vol.39, pp.201-225, 1981.

Y. C. Chang, T. Y. Hou, B. Merriman, and S. Osher, A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows, Journal of Computational Physics, vol.124, issue.2, pp.449-464, 1996.
DOI : 10.1006/jcph.1996.0072

E. Olson and G. Kreiss, A conservative level set method for two phase flow, Journal of Computational Physics, vol.210, issue.1, pp.225-246, 2005.
DOI : 10.1016/j.jcp.2005.04.007

M. Sussman, P. Smereka, and S. Osher, A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow, Journal of Computational Physics, vol.114, issue.1, pp.146-159, 1994.
DOI : 10.1006/jcph.1994.1155

F. Chantalat, C. H. Bruneau, C. Galusinski, and A. Iollo, Level-set, penalization and cartesian meshes: A paradigm for inverse problems and optimal design, Journal of Computational Physics, vol.228, issue.17, pp.228-6291, 2009.
DOI : 10.1016/j.jcp.2009.05.017

URL : https://hal.archives-ouvertes.fr/hal-00385460

F. H. Harlow and J. E. Welsh, Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface, Physics of Fluids, vol.8, issue.12, pp.2182-2189, 1965.
DOI : 10.1063/1.1761178

P. P. Patil and S. Tiwari, Computation of Flow Past Complex Geometries Using MAC Algorithm on Body-Fitted Coordinates, Engineering Applications of Computational Fluid Mechanics, vol.3, issue.1, pp.15-27, 2009.
DOI : 10.1080/19942060.2009.11015251

S. Vincent and J. P. Caltagirone, A One-Cell Local Multigrid Method for Solving Unsteady Incompressible Multiphase Flows, Journal of Computational Physics, vol.163, issue.1, pp.172-215, 2000.
DOI : 10.1006/jcph.2000.6566

C. Galusinski and P. Vigneaux, On stability condition for bifluid flows with surface tension: Application to microfluidics, Journal of Computational Physics, vol.227, issue.12, pp.6140-6164, 2008.
DOI : 10.1016/j.jcp.2008.02.023

URL : https://hal.archives-ouvertes.fr/hal-00274569

G. S. Jiang and D. Peng, Weighted ENO Schemes for Hamilton--Jacobi Equations, SIAM Journal on Scientific Computing, vol.21, issue.6, pp.2126-2143, 2000.
DOI : 10.1137/S106482759732455X

R. Fedkiw, Coupling an Eulerian Fluid Calculation to a Lagrangian Solid Calculation with the Ghost Fluid Method, Journal of Computational Physics, vol.175, issue.1, pp.200-224, 2002.
DOI : 10.1006/jcph.2001.6935

F. Golay and P. Helluy, Numerical schemes for low Mach wave breaking, International Journal of Computational Fluid Dynamics, vol.45, issue.2, pp.69-86, 2007.
DOI : 10.1016/S0021-9991(02)00058-X

URL : https://hal.archives-ouvertes.fr/hal-00139634